Risk is a seemingly simple word that confounds most organizations when it comes to achieving strategic outcomes. We prefer the word uncertainty. Learning about uncertainty starts with developing an understanding of historical efforts to address the concept of probability.
One winter night during one of the many German air raids on Moscow in World War II, a distinguished Soviet professor of statistics showed up in his local air-raid shelter. He had never appeared there before. “There are seven million people in Moscow,” he used to say. “Why should I expect them to hit me?” His friends were astonished to see him and asked what had happened to change his mind. “Look,” he explained, “there are seven million people in Moscow and one elephant. Last night they got the elephant.”
-Peter Bernstein, Against the Gods: The Remarkable Story of Risk, p. 116 (1996)
We began this article series by substituting the concept of uncertainty for risk. Our intent is to dissuade business leaders from thinking of risk as a bad thing. We also want to help the corporate risk management function to be thought of as more than just the “Department of No!” (Credit for renaming the typical risk management function as the Department of No belongs to R. Nason, Rethinking Risk Management, Critically Examining Old Ideas and New Concepts (2017).
A better path is to focus on learning to thrive in a state of uncertainty. Throughout history, humanity has invented various tools and techniques for addressing uncertainty or in other words – increasing the probability and magnitude of good outcomes and decreasing the probability and severity of bad outcomes. In studying uncertainty, probability is the best place to start. The best overview of how humans have learned over time to evaluate probability is Peter Bernstein’s Against the Gods – The Remarkable Story of Risk (1996).
Bernstein teaches us that the history of probability is intertwined with the history of money and the development of applied mathematics and finance. Modern thinking about probability became possible when our species abandoned the belief that uncertainty was simply fate determined by the Gods (ancient Greece) and created the Hindu-Arabic numbering system (500-700 AD). Learning to manage our fate and establishing the field of mathematics set the stage for addressing probability in a systematic way. This is the Renaissance era (1200 AD to 1700 AD) which was dominated by Italian and French thinkers who frequently gleaned insights about probability by trying to solve gambling problems (e.g., calculating the odds of various dice throws). Prominent thinkers included Pierre de Fermat who measured probability through algebra and Blaise Pascal, a mathematics prodigy, who developed tools to measure probability from geometry. Interestingly, Pascal would become a religious zealot, believing that religious devotion was a rational bet on God’s existence and a 50/50 chance of eternal life.
In the 1600s, British thinkers began contributing to the science of probability. Through the work of John Graunt who tabulated statistics on birth and death in London, empirical statistics and actuarial science came to life. Insurance also emerged in two forms: (i) mathematically minded priests in Scotland, looking to take care of widows in their parishes, invented life insurance and (ii) Lloyd’s organized the insurance business in shipping.
The 1700s brought ideas about how to measure uncertainty in decision-making – starting with the contributions of the Bernoulli family of mathematicians who invented various models of rational decision-making. Daniel Bernoulli’s utility model theorized that decisions are made with the goal of maximizing one’s expected satisfaction which is more than a simple calculation of the relative probabilities of various results or returns. Because we have different levels of expected satisfaction (i.e., value), people develop different preferences for dealing with uncertainty. A person who is terrified of lightning may value protection against it – perhaps more than probabilities of a lightning strike would justify. Conversely, if you own something already, you do not value getting more of it as highly as you might value getting something you don’t own (diminishing marginal utility).
The Bernoullis’ contributions to the study of probability led to the creation of today’s edifice of rational decision-making and tools such as regression toward the mean (Francis Galton) and diversification (Harry Markowitz). All of these various ways of measuring probability are rooted in assumptions (e.g., using the past to reason about the future or using statistical sampling to reason about the whole). The challenge is remembering that assumptions are inherently limited in that they describe reality only up to a point. Further, reason and rational behavior represent starting points – not end points – in assessing probability.
This story makes the point. In a letter to his friend Gottfried Leibniz, Jakob Bernoulli questioned how it was possible to know the odds of throwing dice but not know the probability that a man of 20 will outlive a man of 60. Bernoulli proposed to answer the question by examining a large number of pairs of men of each age. Leibniz cautioned his friend against thinking that his proposed study would answer the question with any degree of certainty:
[N]ature has established patterns originating in the return of events but only for the most part. New illnesses flood the human race, so that no matter how many experiments you have done on corpses, you have not thereby imposed a limit on the nature of events so that in the future they could not vary. (Gottfried Leibniz to Jakob Bernoulli, quoted in John Maynard Keynes, A Treatise on Probability (London-Macmillan, 1921).
In short, the Leibniz-Bernoulli exchange is a powerful reminder that probability models are based on inherently-limited assumptions, including the mistaken idea that the future will always be like the past. In the next column, we will examine historical attempts to address probability through commercial insurance.
-Peter Bernstein, Against the Gods: The Remarkable Story of Risk, p. 116 (1996)
We began this article series by substituting the concept of uncertainty for risk. Our intent is to dissuade business leaders from thinking of risk as a bad thing. We also want to help the corporate risk management function to be thought of as more than just the “Department of No!” (Credit for renaming the typical risk management function as the Department of No belongs to R. Nason, Rethinking Risk Management, Critically Examining Old Ideas and New Concepts (2017).
A better path is to focus on learning to thrive in a state of uncertainty. Throughout history, humanity has invented various tools and techniques for addressing uncertainty or in other words – increasing the probability and magnitude of good outcomes and decreasing the probability and severity of bad outcomes. In studying uncertainty, probability is the best place to start. The best overview of how humans have learned over time to evaluate probability is Peter Bernstein’s Against the Gods – The Remarkable Story of Risk (1996).
Bernstein teaches us that the history of probability is intertwined with the history of money and the development of applied mathematics and finance. Modern thinking about probability became possible when our species abandoned the belief that uncertainty was simply fate determined by the Gods (ancient Greece) and created the Hindu-Arabic numbering system (500-700 AD). Learning to manage our fate and establishing the field of mathematics set the stage for addressing probability in a systematic way. This is the Renaissance era (1200 AD to 1700 AD) which was dominated by Italian and French thinkers who frequently gleaned insights about probability by trying to solve gambling problems (e.g., calculating the odds of various dice throws). Prominent thinkers included Pierre de Fermat who measured probability through algebra and Blaise Pascal, a mathematics prodigy, who developed tools to measure probability from geometry. Interestingly, Pascal would become a religious zealot, believing that religious devotion was a rational bet on God’s existence and a 50/50 chance of eternal life.
In the 1600s, British thinkers began contributing to the science of probability. Through the work of John Graunt who tabulated statistics on birth and death in London, empirical statistics and actuarial science came to life. Insurance also emerged in two forms: (i) mathematically minded priests in Scotland, looking to take care of widows in their parishes, invented life insurance and (ii) Lloyd’s organized the insurance business in shipping.
The 1700s brought ideas about how to measure uncertainty in decision-making – starting with the contributions of the Bernoulli family of mathematicians who invented various models of rational decision-making. Daniel Bernoulli’s utility model theorized that decisions are made with the goal of maximizing one’s expected satisfaction which is more than a simple calculation of the relative probabilities of various results or returns. Because we have different levels of expected satisfaction (i.e., value), people develop different preferences for dealing with uncertainty. A person who is terrified of lightning may value protection against it – perhaps more than probabilities of a lightning strike would justify. Conversely, if you own something already, you do not value getting more of it as highly as you might value getting something you don’t own (diminishing marginal utility).
The Bernoullis’ contributions to the study of probability led to the creation of today’s edifice of rational decision-making and tools such as regression toward the mean (Francis Galton) and diversification (Harry Markowitz). All of these various ways of measuring probability are rooted in assumptions (e.g., using the past to reason about the future or using statistical sampling to reason about the whole). The challenge is remembering that assumptions are inherently limited in that they describe reality only up to a point. Further, reason and rational behavior represent starting points – not end points – in assessing probability.
This story makes the point. In a letter to his friend Gottfried Leibniz, Jakob Bernoulli questioned how it was possible to know the odds of throwing dice but not know the probability that a man of 20 will outlive a man of 60. Bernoulli proposed to answer the question by examining a large number of pairs of men of each age. Leibniz cautioned his friend against thinking that his proposed study would answer the question with any degree of certainty:
[N]ature has established patterns originating in the return of events but only for the most part. New illnesses flood the human race, so that no matter how many experiments you have done on corpses, you have not thereby imposed a limit on the nature of events so that in the future they could not vary. (Gottfried Leibniz to Jakob Bernoulli, quoted in John Maynard Keynes, A Treatise on Probability (London-Macmillan, 1921).
In short, the Leibniz-Bernoulli exchange is a powerful reminder that probability models are based on inherently-limited assumptions, including the mistaken idea that the future will always be like the past. In the next column, we will examine historical attempts to address probability through commercial insurance.
RSS Feed